If you want to save old gutters without replacing them, there are a couple of methods that can work for you.
Reseal the Gutters
Gutter sealers can prevent many problems and even fix problems that already exist in old, damaged gutter material. If the gutters leak where sections meet, then get a caulk-like gutter sealer and spread it over the seams. This will prevent more water damage and should stop the leak. If your gutters were installed improperly so that the pieces overlapping on the inside are closer to the downspout and the water hits the crease of the seam, use a second coat of sealer.
Repair the Gutter
If salvaging the gutter goes beyond a coat of sealant, you can still save it and not have to replace it. Even if you have a large hole in the gutter you should be able to repair it. If you have leftover gutter material, cut a piece to cover the hole. If not, you can bend a piece of sheet metal to fit inside the gutter and overlap the edges. Make sure your patch piece big enough to completely overlap and reach at least an inch or two on both sides of the hole. Coat the gutters with roof cement and then press the new piece inside.